A) simple harmonic
B) circle
C) ellipse
D) figure of eight
Correct Answer: C
Solution :
If first equation is \[{{y}_{1}}={{a}_{1}}\sin \omega t\] \[\Rightarrow \] \[\sin \omega t=\frac{{{y}_{1}}}{{{a}_{1}}}\] ?(i) Then second equation will be \[{{y}_{2}}={{a}_{2}}\sin (\omega t+\pi /2)={{a}_{2}}\cos \omega t\] \[\Rightarrow \] \[\cos \omega t=\frac{{{y}_{2}}}{{{a}_{2}}}\] ?(ii) By squaring and adding Eqs. (i) and (ii), we get \[{{\sin }^{2}}\omega t+{{\cos }^{2}}\omega t=\frac{y_{1}^{2}}{a_{1}^{2}}+\frac{y_{2}^{2}}{a_{2}^{2}}\] \[\Rightarrow \] \[\frac{y_{1}^{2}}{a_{2}^{2}}+\frac{y_{2}^{2}}{a_{2}^{2}}=1\] This is the equation of ellipse.
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